Isothermal Chemical Reaction

Consider a tubular reactor where a chemical reaction changes the concentration of the fluid as it moves down the tube. Assuming first-order chemical reaction, isothermal reactor, and constant density, the modeling equation is... 

We start the analysis of CSTRs by considering isothermal operations with single chemical reactions. Isothermal CSTRs are defined as those where Bom = 0in-Since we do not have to determine the reactor temperature, we have to solve only the design equations. The energy balance equation provides tbe heating (or cooling) load necessary to maintain the isothermal conditions. Also, for isothermal operations, the individual reaction rates depend only on the species concentrations, and, when the reactor temperature is taken as the reference temperature, T=To, and Eq. 8.1.5 reduces to... 

Mass transfer with chemical reaction Isothermal effectiveness... 

When using calorimetry for compatibility testing, it is imperative to realise the nonspecific nature of the technique. Several physicochemical processes can give rise to a calorimetric response, including wetting, evaporation, dissolution, crystallisation and chemical reaction. Isothermal microcalorimery has been previously employed to study the degradation kinetics of drugs in solution [49] and in the solid state [50]. Recently [51], isothermal... 

Discussion of the concepts and procedures involved in designing packed gas absorption systems shall first be confined to simple gas absorption processes without compHcations isothermal absorption of a solute from a mixture containing an inert gas into a nonvolatile solvent without chemical reaction. Gas and Hquid are assumed to move through the packing in a plug-flow fashion. Deviations such as nonisotherma1 operation, multicomponent mass transfer effects, and departure from plug flow are treated in later sections. 

Gas—solids fluidization is the levitation of a bed of solid particles by a gas. Intense soflds mixing and good gas—soflds contact create an isothermal system having good mass transfer (qv). The gas-fluidized bed is ideal for many chemical reactions, drying (qv), mixing, and heat-transfer appHcations. Soflds can also be fluidized by a Hquid or by gas and Hquid combined. Liquid and gas—Hquid fluidization appHcations are growing in number, but gas—soHds fluidization appHcations dominate the fluidization field. This article discusses gas—soHds fluidization. 

The Van t Hoff isotherm identifies the free energy relationship for bulk chemical reactions. 

For an isothermal absorber involving a dilute system in which a liquid-phase mass-transfer limited first-order irreversible chemic reaction is occurring, the packed-tower design equation is derived as... 

Most chemical reactions are greatly affected by temperature. The previous chapters discussed reactions at isothermal condition, however, industrial reactors often operate under non-isothermal condition. This is because chemical reactions strongly depend on temperature, either absorbing (i.e., endothermic) or generating (i.e., exothermic) a large amount of heat. 

The rate of a chemical reaction is proportional to the concentration of the reactants, and for a reversible isothermal homogeneous reaction ... 

The simplified equation (for the general equations, see Section IV, L) in the case of unsteady-state diffusion with a simultaneous chemical reaction in isothermal, incompressible dilute binary solutions with constant p and D and with coupled phenomena neglected is... 

Thus, in a reversible process that is both isothermal and isobaric, dG equals the work other than pressure-volume work that occurs in the process." Equation (3.96) is important in chemistry, since chemical processes such as chemical reactions or phase changes, occur at constant temperature and constant pressure. Equation (3.96) enables one to calculate work, other than pressure-volume work, for these processes. Conversely, it provides a method for incorporating the variables used to calculate these forms of work into the thermodynamic equations. 

Which is better for isothermal chemical reactions, pressure driven flow or drag flow between flat plates Assume laminar flow with first-order chemical reaction and compare systems with the same values for the slit width (2Y=H), length, mean velocity, and reaction rate constant. 

For an isothermal system without velocity gradients and chemical reactions, Eq. (36) reduces to... 

Figure 5.4-58. Isothermal DTA runs for 4-nitrobenzoic acid ((reprinted from Grewer (1994), Thermal hazards of chemical reactions . Copyright (1994) with permission from Elsevier Science).

The complex chemical reaction, shown below, is carried out in an isothermal, constant-volume, batch reactor. All the reactions follow simple first-order kinetic rate relationships, in which the rate of reaction is directly proportional to concentration (Fig. 1.3). 

The importance of the Varft Hoff isotherm lies in the fact that it gives the direction of a chemical reaction. If under a given set of conditions AG is positive, then the reaction cannot take place under these conditions. It may, however, occur if the conditions (activities) are suitably altered to make AG negative. 

Heterogeneous chemical reactions in which adsorbed species participate are not pure chemical reactions, as the surface concentrations of these substances depend on the electrode potential (see Section 4.3.3), and thus the reaction rates are also functions of the potential. Formulation of the relationship between the current density in the stationary state and the concentrations of the adsorbing species in solution is very simple for a linear adsorption isotherm. Assume that the adsorbed substance B undergoes an... 

A systematic, rational analysis of both isothermal and nonisothermal tubular systems in which two fluids are flowing must be carried out, if optimal design and economic operation of these pipeline devices is to be achieved. The design of all two-phase contactors must be based on a firm knowledge of two-phase hydrodynamics. In addition, a mathematical description is needed of the heat and mass transfer and of the chemical reaction occurring within a particular system. 

It is convenient to approach the concept of reaction rate by considering a closed, isothermal, constant pressure homogeneous system of uniform composition in which a single chemical reaction is taking place. In such a system the rate of the chemical reaction (r) is defined as ... 

Since these two types of processes have drastically different effects on the conversion levels achieved in chemical reactions, they provide the basis for the development of mathematical models that can be used to provide approximate limits within which one can expect actual isothermal reactors to perform. In the development of these models we will define a segregated system as one in which the first effect is entirely responsible for the spread in residence times. When the distribution of residence times is established by the second effect, we will refer to the system as mixed. In practice one encounters various combinations of these two limiting effects. 

Notice that in the region of fast chemical reaction, the effectiveness factor becomes inversely proportional to the modulus h2. Since h2 is proportional to the square root of the external surface concentration, these two fundamental relations require that for second-order kinetics, the fraction of the catalyst surface that is effective will increase as one moves downstream in an isothermal packed bed reactor. 

The analysis of simultaneous diffusion and chemical reaction in porous catalysts in terms of effective diffusivities is readily extended to geometries other than a sphere. Consider a flat plate of porous catalyst in contact with a reactant on one side, but sealed with an impermeable material along the edges and on the side opposite the reactant. If we assume simple power law kinetics, a reaction in which there is no change in the number of moles on reaction, and an isothermal flat plate, a simple material balance on a differential thickness of the plate leads to the following differential equation... 

The parameter y reflects the sensitivity of the chemical reaction rate to temperature variations. The parameter represents the ratio of the maximum temperature difference that can exist within the particle (equation 12.3.99) to the external surface temperature. For isothermal pellets, / may be regarded as zero (keff = oo). Weisz and Hicks (61) have summarized their numerical solutions for first-order irreversible... 

Geochemical models, as with the approach, are commonly formulated with a variant of the Freundlich isotherm based on a chemical reaction, like Reaction 9.1. In this approach, known as the reaction Freundlich model or the activity Freundlich model, the extent of sorption by the reaction can be expressed,... 

A first-order chemical reaction occurs isothermally in a reactor packed with spherical catalyst pellets of radius R. If there is a resistance to mass transfer from the main fluid stream to the surface of the particle in addition to a resistance within the particle, show that the effectiveness factor for the pellet is given by ... 

The RC1 reactor system temperature control can be operated in three different modes isothermal (temperature of the reactor contents is constant), isoperibolic (temperature of the jacket is constant), or adiabatic (reactor contents temperature equals the jacket temperature). Critical operational parameters can then be evaluated under conditions comparable to those used in practice on a large scale, and relationships can be made relative to enthalpies of reaction, reaction rate constants, product purity, and physical properties. Such information is meaningful provided effective heat transfer exists. The heat generation rate, qr, resulting from the chemical reactions and/or physical characteristic changes of the reactor contents, is obtained from the transferred and accumulated heats as represented by Equation (3-17) ... 

Monte Carlo simulations were carried out to determine the free energy curve for the reaction in solution. The simulations were executed for the solute surrounded by 250 water molecules (or 180 DMF molecules) in the isothermal-isobaric ensemble at 25 °C and 1 atm, including periodic boundary conditions. As a consequence, the Gibbs free energy is obtained in this case. There is sufficient solvent to adequately represent the bulk participation in the chemical reaction. 

For isothermal, first-order chemical reactions, the mole balances form a system of linear equations. A non-ideal reactor can then be modeled as a collection of Lagrangian fluid elements moving independe n tly through the system. When parameterized by the amount of time it has spent in the system (i.e., its residence time), each fluid element behaves as abatch reactor. The species concentrations for such a system can be completely characterized by the inlet concentrations, the chemical rate constants, and the residence time distribution (RTD) of the reactor. The latter can be found from simple tracer experiments carried out under identical flow conditions. A brief overview of RTD theory is given below. 

For non-linear chemical reactions, this term leads to new unclosed terms that are difficult to model. For example, even the isothermal second-order reaction, (3.142), where the joint dissipation chemical source term is given by... 

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